Use a mathematical model that estimates vibration at the top bearing of a motor used on a vertical, wet-pit, column type pump.

## The Results

• From Equation 1 and Figure 2, the vibration response is dominated by the frequency ratio (frequency separation margin).
• Vibration response varies linearly with the motor balance grade. This is expected from Equation 1, and the results in Tables 1 and 2 confirm this. Note that a motor balance grade of G2.5 yields values 40 percent of those achieved with balance grade G6.3.
• From Tables 1 and 2, the vibration response obtained is constant across different pump design operating speeds when units of velocity are used. This is expected because the excitation is constant velocity-based values of motor imbalance (balance grade). Usually higher speeds involve smaller pumps and slower speeds involve larger pumps. The results encompass a range of pump sizes. The topic of units of vibration useful for the purpose of standard acceptance criteria is discussed in the second part of this series.
• From Tables 1 and 2, the vibration response obtained with units of mils peak-to-peak is not constant but varies with the design operating speed. Again, the results encompass a range of pump sizes. The topic of units of vibration useful for the purpose of standard acceptance criteria is discussed in the second part of this series.
• A frequency separation margin of 10 percent (obtained in the field by test) produces a range of vibration responses at the top motor bearing that are reasonable.
Table 1. Results from example one
Table 2. Results from example two

## Implications of the Results

• As shown in Equation 1 and Tables 1 and 2 with the structure reed frequency field characteristics fixed and assumed to be based on test, no inputs for top-of-motor bearing height, structural rigidity or foundation rigidity considerations are used to calculate the vibration response. Analysis of empirical field data to determine top-of-motor bearing vibration acceptance criteria should not consider these parameters, nor should acceptance criteria be based on these parameters.
• When the field structure reed frequency characteristics (based on test) are not known and are determined by calculation (such as in the pre-construction phase of a project), height and rigidity characteristics impact the value of the calculated structure reed frequency as discussed in the September 2012 article. The calculated reed frequency is included in Equation 1, with no subsequent consideration of structure height or structure rigidity.
• Predicting accurate structure reed frequencies in the pre-construction phase is important to achieve an acceptable frequency ratio.
• Because of the inaccuracies of the available structure reed frequency calculation methods, frequency separation ratio values higher than ±10 percent should be used to obtain actual separation ratio values in the field of ±10 percent when the structure reed frequency is calculated.
• To determine the structure reed frequency in the preconstruction stage and because the motor reed frequency dominates the structure reed frequency result, the motor reed frequency provided by the motor vendor must be accurate.
• Typically, different field vibration levels are measured in line with the axis of the piping versus perpendicular to the axis of the piping. This is because of the different field structure reed frequency characteristics relating to the different directions and corresponding different frequency ratio values (or frequency separation margins) that result in the different responses.

The second part of this series (April 2014) includes guidelines for reducing top-of-motor vibration, the effects of the pump’s foundation on vibration and operation speed considerations.

## References

1. Claxton, J. “Top-of-Motor Vibration,” Pumps and Systems, September 2012.
2. ANSI/HI 9.6.8, Dynamics of Pumping Machinery, Hydraulic Institute, Parsippany, N.J., www.pumps.org.